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C₂×#612634 #72293989

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

157869 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(11,12)(13,15)(14,17)(16,18)(19,20)(21,25)(22,23)(24,26);(11,13,14,18)(12,15,17,16)(19,21)(20,24)(22,25)(23,26);(4,6)(8,10)(11,13)(12,16)(14,18)(15,17)(19,22,23,20)(21,25,26,24);(7,8)(9,10);(3,4)(5,6)(7,8)(9,10)(11,12)(13,15)(14,17)(16,18)(19,21)(20,25)(22,24)(23,26);(1,2)

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((11,12)(13,15)(14,17)(16,18)(19,20)(21,25)(22,23)(24,26), (11,13,14,18)(12,15,17,16)(19,21)(20,24)(22,25)(23,26), (4,6)(8,10)(11,13)(12,16)(14,18)(15,17)(19,22,23,20)(21,25,26,24), (7,8)(9,10), (3,4)(5,6)(7,8)(9,10)(11,12)(13,15)(14,17)(16,18)(19,21)(20,25)(22,24)(23,26), (1,2));